|
|
A166364
|
|
Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
|
|
1
|
|
|
1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593735, 292968600, 1464842640, 7324211400, 36621048000, 183105195000, 915525750000, 4577627625000, 22888132500000, 114440634375000, 572203031250000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The initial terms coincide with those of A003948, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (4,4,4,4,4,4,4,4,4,4,-10).
|
|
FORMULA
|
G.f.: (t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
|
|
MAPLE
|
seq(coeff(series((1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020
|
|
MATHEMATICA
|
CoefficientList[Series[(1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12), {t, 0, 30}], t] (* G. C. Greubel, May 10 2016 *)
|
|
PROG
|
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12) ).list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|